Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1536 conjugacy classes of subgroups.
The subgroup lattice has 321 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589395 | C2 | direct (N × H) |
| 11. C2×C32×C4⋊C4 | C4 | semidirect |
| 15. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 19. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 44. C32×C4⋊C4 | C2×C4 | semidirect |
| 47. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 51. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 58. C2×C3×C4⋊C4 | Dic3 | semidirect |
| 121. C3×C4⋊C4 | C2×Dic3 | semidirect |
| 163. C2×C4⋊C4 | C3⋊Dic3 | semidirect |
| 195. C2×C32 | #340 | semidirect |
| 229. C4⋊C4 | C2×C3⋊Dic3 | semidirect |
| 251. C32 | C2×#340 | semidirect |
| 282. C2×C3 | #4529 | semidirect |
| 311. C3 | C2×#4529 | semidirect |
| 312. C2 | #10589395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4⋊C4 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C23×C3⋊(C3⋊C8) | 2 |
| #10589395 | 2 |
| C2×#4529 | 3 |